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Article Dans Une Revue Physical Review Fluids Année : 2024

Viscous rebound of a quasi-two-dimensional cylinder on a solid wall


The purpose of the present study is to extend the simple concept of apparent coefficient of restitution, widely approached in the literature for the case of a single contact point between a sphere and a wall, to the case of bouncing whose complexity is increased due to the shape of the contacting object. For this purpose, experiments are carried out with a finite-length cylinder, freely falling in a liquid at rest. A rigid tail is attached to the cylinder, allowing one to maintain a vertical trajectory and to keep the axis of the cylinder parallel to the bottom wall down to a small gap between them. Yet, more complex 3D motions of the cylinder with respect to the wall occur during bouncing, including multiple-contact-point bouncing between the cylinder and the bottom as well as cavitation. When the Stokes number St (the ratio between characteristic inertial forces experienced by the particle compared to viscous forces in the fluid) is increased, the experimental results suggest that the ratio of the apparent coefficient of restitution to the solid one increases from 0 (at low St) to 1 (at large St) with a critical Stokes number Stc below which no bouncing is observed, as usually obtained in the literature for a single-contact-point bouncing sphere. In a conceptual approach to understanding the observed experimental features using a cutoff length scale prior to contact and a contact timescale, we investigated numerical modeling of an idealized situation, a 2D infinite cylinder falling parallel to the wall. To this end, we carried out numerical 2D simulations where the fluid equations of motion were coupled to the particle equation of motion through an immersed boundary method. The particle equation of motion was coupled to an elastic force to model bouncing. This numerical model requires parametrization of the cutoff length (interpreted as a roughness) and the contact time (associated with the contact elasticity) used here to capture the experimental observations. The simulations confirmed that (1) the departure of the coefficient of restitution from 0 is strictly dependent on the apparent roughness and (2) the coefficient of restitution depends on the contact time. Finally, in an effort to rationalize the experiments and the simulations for such a conceptual approach, we modeled the coefficient of restitution as the product of two contributions to the mechanical loss of energy: the collision-to-terminal velocity ratio (Vc/Vt) of the approach phase and the rebound-to-collision velocity ratio (−Vr/Vc) of the contact phase. We then interpreted the experimental measurements in light of this model, showing evidence that the assumption of a global relationship between the contact time and an apparent roughness (all being linked to the bouncing complexity including multiple-contact-point and cavitation in experiments) leads to a reasonably good prediction of the coefficient of restitution in the intermediate regime in St. This suggests the relevance of lumping the complex details of physical phenomena involved during contact into a simple concept based on the contact apparent roughness and elasticity.
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Dates et versions

hal-04578655 , version 1 (17-05-2024)



Alicia Aguilar-Corona, Micheline Abbas, Matthieu J. Mercier, Laurent Lacaze. Viscous rebound of a quasi-two-dimensional cylinder on a solid wall. Physical Review Fluids, 2024, 9 (4), pp.044301. ⟨10.1103/physrevfluids.9.044301⟩. ⟨hal-04578655⟩
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